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0580/32 Feb/Mar 2024, Question 2: Mean, Median, Mode and Range

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 18 marks

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The question, in short

Fuel prices at two garages are given; answer questions on change, cost difference, mean litres, percentage rise, tank capacity, litre-gallon conversion and cylindrical tank volume.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Find the change from $100 after buying 55 litres at $1.41 per litre.

  1. 1Cost = 55 × 1.41 = $77.55
  2. 2Change = 100 − 77.55 = $22.45

Answer22.45

Part (aii) · 2 marks

Find how much less 20 litres costs at $1.41 than at $1.50 per litre.

  1. 1Garage B: 20 × 1.50 = $30
  2. 2Garage A: 20 × 1.41 = $28.20
  3. 3Difference = 30 − 28.20 = $1.80

Answer1.80

Part (aiii) · 3 marks

Given six amounts spent at $1.41 per litre, find the mean number of litres bought.

  1. 1Total spent = 63 + 84.50 + 72.23 + 46 + 54.10 + 80 = $399.83
  2. 2Total litres = 399.83 ÷ 1.41 = 283.56…
  3. 3Mean = 283.56… ÷ 6 = 47.26…
  4. 4= 47.3 litres

Answer47.3 or 47.26…

Part (aiv) · 2 marks

Find the percentage increase when the price rises from $1.50 to $1.53.

  1. 1Increase = 1.53 − 1.50 = 0.03
  2. 20.03 ÷ 1.50 × 100 = 2%

Answer2

Part (b) · 3 marks

A tank is 2/5 full and needs 39 more litres; find the full capacity in litres.

  1. 1Empty part = 1 − 2/5 = 3/5 of the tank
  2. 23/5 of the tank = 39 litres
  3. 31/5 = 39 ÷ 3 = 13 litres
  4. 4Full tank = 13 × 5 = 65 litres

Answer65

Part (ci) · 2 marks

Using 1 litre = 0.22 gallons, complete the conversion graph of litres against gallons.

  1. 1100 litres = 100 × 0.22 = 22 gallons
  2. 2Plot (0, 0) and (100, 22)
  3. 3Join them with a ruled straight line

AnswerA straight line through (0, 0) and (100, 22)

Part (cii) · 1 mark

Using 1 litre = 0.22 gallons, state how many litres equal 1 gallon.

  1. 11 gallon = 1 ÷ 0.22 litres
  2. 2= 4.545… = 4.55 litres

Answer4.55 or 4.545…

Part (d) · 3 marks

Find the volume in litres of a cylinder with radius 1.5 m and height 8 m.

  1. 1V = π × 1.5² × 8
  2. 2= 56.548… m³
  3. 31 m³ = 1000 litres
  4. 456.548… × 1000 = 56 500 litres (56 548.6…)

Answer56500, 56600 or 56540 to 56560

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